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First, make the Muddy Buddies. Add the chex to a large mixing bowl and set off to the side. Line a large baking sheet with wax paper and set off to the side.
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In a medium microwave safe mixing bowl, combine the chocolate chips, peanut butter, and butter. Microwave for 30 seconds and then stir until smooth. Microwave for another 10-20 seconds if still not smooth and melted. Stir in the vanilla.
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Pour the melted chocolate peanut butter mixture over the chex cereal. Mix until all the cereal is evenly coated.
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Transfer the coated cereal to a large gallon sized sealable plastic storage bag. Add in the powdered sugar. Seal the bag and then shake to coat evenly.
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Once coated, dump the mixture on to the prepared baking sheet. Spread out in one even layer and let cool.
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While your Muddy Buddies cool, make the ice cream base.
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Whisk together the condensed milk, vanilla paste, and salt in a large mixing bowl.
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In the bowl of an electric stand mixer fitted with the whisk attachment, beat the cream cheese on medium until smooth.
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Turn the mixer to low and slowly stream in the heavy cream. Increase the speed to medium/high and mix until stiff peaks form, about 4 minutes.
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Add half the whipped cream to the milk mixture. Whisk until completely combined.
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Gently fold in the remaining whipped cream using a rubber spatula. This will take about 7-10 minutes until well combined and no streaks remain.
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Fold in the Muddy Buddies. They don't even need to be all covered in the cream mixture.
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Pour into a 9-inch loaf pan or Pullman pan with a lid.
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Place small dollops of the nutella and peanut butter on the top of the ice cream mixture. Use a fork or wooden skewer to gently swirl the dollops around.
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Cover with plastic wrap or lid and freeze for at least six hours. Once frozen, ice cream will keep for a week.